Abstract
The algebra SU(2)q is realized by q-differential operators on polynomials in two variables. The method of van der Waerden for computing SU(2) C.G. coefficients is generalized to SU(2)q.
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References
V. Drinfeld, Dokl. Akad. Nauk USSR 283, 1060 (1985). M. Jimbo, Lett. Math. Phys. 10, 63 (1985) and 11, 247 (1986). E. Sklyanin, Usp.Mat.Nauk, 214, N2 (1985). V. Drinfeld, Proceed. Int. Congr. Math. Berkeley, Ed. A.M.Gleason, AMS, Providence 798 (1987). S.L. Woronowicz, Publ. R.I.M.S., Kyoto Univ., 23, 117 (1987). Yu. I. Manin, Quantum Groups and Non-commutative Geometry, Les publications CRM, Montréal 1988.
P.P. Kulish and N. Reshetikhin, J. Soviet Math. 23, 2435 (1983). Russian original:“Zapiski Nauch” Semin. LOMI 101, 101 (1981).
F.N. Jackson, Quart. J. Pure a. Appl. Math. 41, 193 (1910).
L. Alvarez-Gaumé, C. Gomez and G. Sierra, Nucl. Phys. B. To appear. L. Alvarez-Gaumé, C. Gomez and G. Sierra, Phys. Lett. 220, 142 (1989). L. Alvarez-Gaumé, C. Gomez and G. Sierra, Duality and Quantum Groups, Preprint CERN-TH 5369/89 UGVA-DPT-3/605/89 (1989).
H. Ruegg, A simple derivation of the quantum Clebsch Gordan coefficients for SU(2)q, J. Math. Phys. (1990).
B.L. van der Waerden, Die Gruppentheoretische Methode in der Quantenmechanik, Springer, Berlin 1932. English Translation, Group Theory and Quantum Mechanics, Springer 1974.
An expression similar but not identical to (2.10), using a different basis, has been obtained by A.Ch. Ganchev and V. B. Petkova, Preprint IC/89/158 (revised) (1989).
A.N. Kirillov and N. Reshetikhin, LOMI preprint E-9-88 (1988).
Bo-Yu Hou, Bo-Yuan Hou and Zhong-Qi Ma, Preprints BIHEP-TH-89-7-NWU-IMP-89-11 and BIHEP-TH-89-8 NWU-IMP-89-12 (1989).
A.R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton Univ. Press 1957, p. 45, Equ. (3.6.11).
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Ruegg, H. (1990). Polynomial basis for SU(2)q and Clebsch-Gordan coefficients. In: Doebner, H.D., Hennig, J.D. (eds) Quantum Groups. Lecture Notes in Physics, vol 370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53503-9_42
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DOI: https://doi.org/10.1007/3-540-53503-9_42
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